Subspaces of Multisymplectic Vector Spaces

Abstract

A notion of orthogonality in multisymplectic geometry has been developed by Cantrijn, Ibort and de León and used by many authors. In this paper, we review this concept and propose a new type of orthogonality in multisymplectic geometry; we prove a number of results regarding this orthogonality and its associated subspaces. We end by calculating the various subspaces of a G_2-vector space based on both types of orthogonality.

LaTeX2e; 13 pages

References in corpus (4)

• Closed forms and multi-moment maps
• Higher Symplectic Geometry
• Classical field theories of first order and lagrangian submanifolds of premultisymplectic manifolds
• The notion of Observables in Multisymplectic Geometry

Cited by in corpus (1)

• An Almost Contact Structure on $G_2$-Manifolds